Strictly cyclic algebra of operators acting on Banach spaces $H^p\left(\beta \right)$

Yousefi, Bahmann. "Strictly cyclic algebra of operators acting on Banach spaces $H^p(\beta )$." Czechoslovak Mathematical Journal 54.1 (2004): 261-266. <http://eudml.org/doc/30856>.

@article{Yousefi2004,
abstract = {Let $\lbrace \beta (n)\rbrace ^\{\infty \}_\{n=0\}$ be a sequence of positive numbers and $1 \le p < \infty $. We consider the space $H^\{p\}(\beta )$ of all power series $f(z)=\sum ^\{\infty \}_\{n=0\}\hat\{f\}(n)z^\{n\}$ such that $\sum ^\{\infty \}_\{n=0\}|\hat\{f\}(n)|^\{p\}\beta (n)^\{p\} < \infty $. We investigate strict cyclicity of $H^\{\infty \}_\{p\}(\beta )$, the weakly closed algebra generated by the operator of multiplication by $z$ acting on $H^\{p\}(\beta )$, and determine the maximal ideal space, the dual space and the reflexivity of the algebra $H^\{\infty \}_\{p\}(\beta )$. We also give a necessary condition for a composition operator to be bounded on $H^\{p\}(\beta )$ when $H^\{\infty \}_\{p\}(\beta )$ is strictly cyclic.},
author = {Yousefi, Bahmann},
journal = {Czechoslovak Mathematical Journal},
keywords = {the Banach space of formal power series associated with a sequence $\beta $; bounded point evaluation; strictly cyclic maximal ideal space; Schatten $p$-class; reflexive algebra; semisimple algebra; composition operator; Banach space of formal power series associated with a sequence; bounded point evaluation; strictly cyclic maximal ideal space; Schatten -class; reflexive algebra; semisimple algebra; composition operator},
language = {eng},
number = {1},
pages = {261-266},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Strictly cyclic algebra of operators acting on Banach spaces $H^p(\beta )$},
url = {http://eudml.org/doc/30856},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Yousefi, Bahmann
TI - Strictly cyclic algebra of operators acting on Banach spaces $H^p(\beta )$
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 261
EP - 266
AB - Let $\lbrace \beta (n)\rbrace ^{\infty }_{n=0}$ be a sequence of positive numbers and $1 \le p < \infty $. We consider the space $H^{p}(\beta )$ of all power series $f(z)=\sum ^{\infty }_{n=0}\hat{f}(n)z^{n}$ such that $\sum ^{\infty }_{n=0}|\hat{f}(n)|^{p}\beta (n)^{p} < \infty $. We investigate strict cyclicity of $H^{\infty }_{p}(\beta )$, the weakly closed algebra generated by the operator of multiplication by $z$ acting on $H^{p}(\beta )$, and determine the maximal ideal space, the dual space and the reflexivity of the algebra $H^{\infty }_{p}(\beta )$. We also give a necessary condition for a composition operator to be bounded on $H^{p}(\beta )$ when $H^{\infty }_{p}(\beta )$ is strictly cyclic.
LA - eng
KW - the Banach space of formal power series associated with a sequence $\beta $; bounded point evaluation; strictly cyclic maximal ideal space; Schatten $p$-class; reflexive algebra; semisimple algebra; composition operator; Banach space of formal power series associated with a sequence; bounded point evaluation; strictly cyclic maximal ideal space; Schatten -class; reflexive algebra; semisimple algebra; composition operator
UR - http://eudml.org/doc/30856
ER -